Typically, one in six detergent packages is not properly packaged. In a sample, 10 pieces are randomly checked. How big is the Probability that (a) none, (b) more than 5 of the checked packages are not properly packaged?



Answer to a math question Typically, one in six detergent packages is not properly packaged. In a sample, 10 pieces are randomly checked. How big is the Probability that (a) none, (b) more than 5 of the checked packages are not properly packaged?

Expert avatar
62 Answers
Wir können dieses Problem mithilfe der Binomialverteilung lösen. Die Formel für die Binomialverteilung ist gegeben durch:

P(X = k) = \binom{n}{k} \cdot p^k \cdot (1-p)^{n-k}

- n die Anzahl der Versuche ist,
- k die Anzahl der Erfolge ist,
- p die Wahrscheinlichkeit eines Erfolges ist.

In diesem Fall ist n = 10 (Anzahl der überprüften Verpackungen) und p = \frac{1}{6} (Wahrscheinlichkeit, dass eine Verpackung nicht ordnungsgemäß verpackt ist).

(a) Die Wahrscheinlichkeit, dass keine der überprüften Verpackungen nicht ordnungsgemäß verpackt sind ist gegeben durch:

P(X = 0) = \binom{10}{0} \cdot \left(\frac{1}{6}\right)^0 \cdot \left(1-\frac{1}{6}\right)^{10-0}

P(X = 0) = 1 \cdot 1 \cdot \left(\frac{5}{6}\right)^{10}

P(X = 0) = \left(\frac{5}{6}\right)^{10} \approx 0.1615

Frequently asked questions (FAQs)
Question: Given the sides of a triangle as 5, 7, and 9 units, what is the area of the triangle using Heron's Formula?
Find the equation of a parabola with vertex at (2, -3) and passing through the point (4, 5).
What is the area of a rectangle if its length is 10 units and its width is 5 units?
New questions in Mathematics
I want to divide R$ 2200.00 between Antônio, Beto and Cássia, so that Beto receives half from Antônio and Cássia receives a third of Beto. Under these conditions, how much more will Beto receive than Cássia?
5/8 x 64
10.Silvana must knit a blanket in 9 days. Knitting 8 hours a day, at the end of the fifth day, only 2/5 of the blanket was done. To be able to finish on time, how many hours will Silvana have to knit per day?
For a temperature range between -3 degrees Celsius to 5 degrees Celsius, what is the temperature range in degrees Farenheight
A food delivery company charges on average a delivery fee of $5 per order (including food and shipping) and has monthly fixed costs of $600. If the average cost of each meal delivered that is revenue for the company is $10 and the company has a monthly profit of $800, how many orders must they deliver per month?
A bird randomly chooses to land on 1 of 12 perches available in its aviary. Determine the Probability of it landing on a perch numbered 8 and then on a perch marked with a prime number; take into account that he never lands on the same perch in the sequence.
The durability of a tire of a certain brand is a Normal random variable with an average of 64,000 km and a standard deviation of 9,000 km. Assuming independence between tires, what is the probability that the 4 tires on a car will last more than 58,000 km?
form a key for your lock containing the numbers 2 2 5 8 How many different keys can you form?
. What will be the osmotic pressure of a solution that was prepared at 91°F by dissolving 534 grams of aluminum hydroxide in enough water to generate 2.784 ml of solution.
show step by step simplification: (¬𝑑∨((¬b∧c)∨(b∧¬c)))∧((𝑎 ∧ 𝑏) ∨ (¬𝑎 ∧ ¬𝑏))∧(¬𝑐∨((¬𝑑∧𝑎)∨(𝑑∧¬𝑎)))
Convert 9/13 to a percent
Solve the following equation for x in exact form and then find the value to the nearest hundredths (make sure to show your work): 5e3x – 3 = 25
A machine produces 255 bolts in 24 minutes. At the same rate, how many bolts would be produced in 40 minutes?
2)A tourist has 15 pairs of pants in his hotel room closet. Suppose 5 are blue and the rest are black. The tourist leaves his room twice a day. He takes a pair of pants and puts them on, the tourist leaves the first pair of pants in the closet again and takes another one and puts them on. What is the probability that the two pants chosen are black?
A block slides across the floor with a force of 20N, which has an angle of 30°. The mass of the block is 2kg and the coefficient of friction is 0.1. Calculate the value of all the forces involved in this system and finally the value of the acceleration.
Find I (Intrest) using simple interest formula of 17700 @ 15% for 4 years
The average weekly earnings in the leisure and hospitality industry group for a re‐ cent year was $273. A random sample of 40 workers showed weekly average ear‐ nings of $285 with the population standard deviation equal to 58. At the 0.05 level of significance can it be concluded that the mean differs from $273? Find a 95% con‐ fidence interval for the weekly earnings and show that it supports the results of the hypothesis test.
answer this math question The scale on a map is drawn so that 5.5 inches corresponds to an actual distance of 225 miles. If two cities are 12.75 inches apart on the map, how many miles apart are they? (Round to the nearest tenth) miles apart. The two cities are how many miles apart
Convert (324)𝑓𝑖𝑣𝑒 into base-ten